You visited us 1 times! Enjoying our articles? Unlock Full Access!

Hydrosphere and the Distribution of Water

Which of the ...

Question

Which of the following is the negation of the statement "for all $M > 0,$ there exists $x \in S$ such that $x \geq M$ " ?

There exists

M > 0

, there exists

x \in S

such that

x < M

No worries! We‘ve got your back. Try BYJU‘S free classes today!

There exists

M > 0

, there exists

x \in S

such that

x \geq M

No worries! We‘ve got your back. Try BYJU‘S free classes today!

There exists

M > 0

, such that

x < M

for all

x \in S

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

There exists

M > 0

, such that

x \geq M

for all

x \in S

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C There exists $M > 0$ , such that $x < M$ for all $x \in S$
Statement : For all $M > 0$ , There exists $x \in S$ such that $x \geq M$ .
Negation : There exists $M > 0$ , such that $x < M$ for all $x \in S$ .

Suggest Corrections

Similar questions

Q. Let

S

be a non-empty subset of

R

Consider the following statement:

P :

There exist's a rational number

x \in S

such that

x > 0.

Which of the following statements is the negation of the statement

P ?

Q. Let

S

be a non-empty subset of

R .

Consider the following statement :

P :

There exists a rational number

x \in S

such that

x > 0.

Which of the following statements is the negation of the statement

P

The negation of the statement “p: For every real number x, x³ > x².” is:

Q. Which of the following is the negation of the statement, For all odd primes

p < q

there exists positive non-primes

r < s

such that

p^{2} + q^{2} = r^{2} + s^{2}

Write the negation of the following statements :

(i) p : For every positive real number x, the number x - 1 is also positive.

(ii) q : All cats scratch.

(iii) r : For every real number x, either x > 1 or x < 1.

(iv) s : There exists a number x such that 0 < x < 1.

Join BYJU'S Learning Program

Which of the following is the negation of the statement "for all M>0, there exists x∈S such that x≥M" ?

The correct option is C There exists M>0, such that x<M for all x∈SStatement : For all M>0, There exists x∈S such that x≥M. Negation : There exists M>0, such that x<M for all x∈S.

Which of the following is the negation of the statement "for all $M > 0,$ there exists $x \in S$ such that $x \geq M$ " ?

The correct option is C There exists $M > 0$ , such that $x < M$ for all $x \in S$
Statement : For all $M > 0$ , There exists $x \in S$ such that $x \geq M$ .
Negation : There exists $M > 0$ , such that $x < M$ for all $x \in S$ .